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N-fold sums of Cantor sets

Part of:Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Kathryn E. Hare and
Toby C. O'Neil
Kathryn E. Hare
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1. E-mail: kehare@uwaterloo.ca
Toby C. O'Neil
Affiliation:
Department of Pure Mathematics, Faculty of Maths and Computing, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK. E-mail: t.c.oneil@open.ac.uk
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Abstract

The Newhouse gap lemma is generalized by finding a geometric condition which ensures that N-fold sums of compact sets, which might even have thickness zero, are intervals. A new proof is also obtained of a lower bound on the thickness of the sum of two Cantor sets.

MSC classification

Secondary:28A80: Fractals

Information

Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000, pp. 243 - 250
Copyright
Copyright © University College London 2000

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References

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